"To which real questions about the foundations of mathematics does
humanism hold the key?"
None, as near as I can tell.
Would you ask a basketball player how many home runs and stolen bases he
scored?
Or a meteorologist, how many quarks he captured today?
Or go in the hardware department for oranges and lemons?
I specifically renounced any ambitions or pretensions in f.o.m.
I claimed that philosophy of mathematics is not idential with
f.o.m. I claim it is possible to clarify philosophical
issues about math without contributing to f.o.m. My attempt
is to clarify how it is that mathematics is real and meaningful,
without resorting to mysticism, myth, superstition or theology.
I gladly acknowledge the unforgettable, indispensable contributions
of Frege, Hilbert, Brouwer and others to the foundations of mathematics.
Interestingly, the worth of these contributions is not lessened
by the fact that logicism, formalism, and intuitionism each
saw only a portion of what mathematiacs is. By claiming that
their partial picture was the whole story, all three became
incomplete, misleading, false. It is not heaping scorn to
acknowledge their philosophical failures along with their
mathematical achievements.
Zei gezunt.
Reuben